Calculation of Electric fields in Electrical Tree Channels

Trapped charges namely, the electrons and ions would be present in the bulk and surface of solid insulation, due to electrical stressing or other reasons. These charges modify the main field (MF), thereby affecting the initiation and growth of electrical trees. Whenever the total stress due to the MF and the Local Field (LF) exceeds the critical stress at any point, the physical and molecular structure is broken and a channel (tubule) is formed. Initiation of breakdown here is defined as the appearance of the breakdown channel (tubule) followed by the growth of further breakdown channels, either in the form of branch type trees with well defined branches or bushes consisting of an aggregate of large number of fine tubules. The field condition at any point is dependent on the MF and the charges on the tubules and their orientation. The effect of the tubules on the field distribution in the needle-plane gap may be estimated, by defining charges located suitably and calculating the fields thus simulated. In this work, a PMMA sample aged at 50Hz A.C. that had developed electrical trees was selected. The electrical field resulting from the superposition of main field (needle-plane) and the tubules (implying tree channels) is calculated and the estimation of future growth direction is presented.